I'm traveling from the US, through Munich Airport, to connect to another flight to Turkey. What exactly is checked when going through passport control in the Munich Airport?
You are transferring from a flight from a non-Schengen location to a flight to a non-Schengen location. Your passport will be checked, so you need to have it and a valid visa if necessary. You may need to have a copy of the documents that you needed to obtain the visa, such as your ticket or boarding pass for your onward flight (proof of onward travel). There are two cases when changing airplanes inside the Schengen area:
The official information from the German embassy is that Munich has an international area, so you only need a transit visa at most unless you want to get out of the airport.
Whether you need a transit visa depends on your nationality. USA citizens don't need one; Turkish citizens generally do. However, if you are Turkish (or from a number of other countries) and hold a valid visa or residence permit for the US (or if your US visa expired less than 4 days ago) then you do not need a transit visa.
Munich airport allows International to International transfers without having to pass through passport control.
There are however a small number of countries that may require a visa to pass through the airport, even if you are not going through passport control - and that includes Turkish citizens.